基于张量CP分解的高频数据波动率矩阵预测  

Prediction of High-Frequency Data Volatility Matrix Based on Tensor CP Decomposition

作　　者：张晨琳 仝硕 

机构地区：[1]南京审计大学经济学院,江苏 南京 [2]南京审计大学统计与数据科学学院,江苏 南京

出　　处：《管理科学与工程》2023年第5期724-737,共14页Management Science and Engineering

摘　　要：随着计算机技术的高速发展,高频数据的获取与存储不再是件难事,研究发现由于高频数据波动率矩阵包含了更多的信息,基于其估计的协方差会更加准确。高频数据的使用带来了微观结构噪声影响,并且资产的波动性具有较强的记忆性和持续性,投资者有异质特征,传统波动率矩阵的估计方法效果并不理想。同时,当总体维数超过样本容量时,传统的估计方法会面临维数灾难的问题。与以往预测方法不同,本文利用张量能够存储多维度信息、结构稳定等优点,与HAR模型相结合提出CP-HAR模型预测高频波动率矩阵。该模型构建思路为:首先计算T天的高频波动率矩阵Σ1,Σ2,……,ΣT并按天数“堆积”得到一个三阶张量X∈RTxIxJ,随后对该三阶张量CP分解,对其中刻画时间维度方向的因子矩阵深入探究,即利用HAR模型对其中T个时间序列的向量进行动态自回归建模,得到预测矩阵。最后通过得到的预测矩阵与前面CP分解得到的另外两个因子矩阵合并组成新张量Xn∈RFxIxJ,拆分看为F个IxJ的高频波动率矩阵即为预测的高频波动率矩阵。实证分析部分,选取沪深300成分股每5分钟高频数据,在资本资产定价Fama-French三因子模型的基础上,利用市值、账面市值比两个具有强解释能力的因子将所有股票分为25组,以每组为单位计算波动率矩阵并通过CP-HAR模型进行高频波动率矩阵的预测,得到65个波动率预测矩阵,并选取常见指标RMSE、MAE、MAPE以及R2评价预测效果。With the rapid development of computer technology, obtaining and storing high-frequency data is no longer a difficult task. Research has found that due to the volatility matrix of high-frequency data containing more information, the estimated covariance based on it will be more accurate. The use of high-frequency data brings about the impact of microstructure noise, and the volatility of assets has strong memory and persistence. Investors have heterogeneous characteristics, and the estimation methods of traditional volatility matrices are not ideal. At the same time, when the total dimension exceeds the sample size, the traditional estimation methods will face the problem of Curse of dimensionality. Different from previous prediction methods, this paper proposes a CP-HAR model to predict high-frequency volatility matrix by combining the advantages of tensors such as being able to store multi-dimensional information and having a stable structure with the HAR model. The construction idea of this model is as follows: First, calculate the high-frequency volatility matrix Σ1, Σ2, …, ΣT for T days and “stack” it by days to obtain a third order tensor X∈RTxIxJ Then, we decompose the third order tensor CP and deeply explore the factor matrix that depicts the direction of the time dimension. That is, we use the HAR model to dynamically autoregressive model the vectors of T time series to obtain a prediction matrix. Finally, the prediction matrix obtained is combined with the other two factor matrices obtained from the previous CP decomposition to form a new tensor Xn∈RFxIxJ , The high frequency volatility matrix of F IxJ is the predicted high frequency volatility matrix. In the empirical analysis section, high-frequency data of 300 constituent stocks in Shanghai and Shenzhen are selected every 5 minutes. Based on the capital asset fixed Fama French three factor model, all stocks are divided into 25 groups using two strong explanatory factors: market value and book to market ratio. The volatility matrix is cal

关 键 词：高频数据波动率矩阵 张量CP分解 HAR模型 波动率矩阵 预测效果评价 

分 类 号：O15[理学—数学]